Extreme cases: ionic compounds (LiF)
orbitals
A1
A1
Li transfers e- to F,
forming Li+ and F-.
This means it occupies
a MO centered on the F
Molecular orbitals for larger molecules
1. Determine point group of molecule (if linear, use D2h and C2v instead of D∞h or C∞v)
2. Assign x, y, z coordinates
(z axis is higher rotation axis; if non-linear y axis in outer atoms point to central atom)
3. Find the characters of the reducible representation for the combination of 2s orbitals on
the outer atoms, then for px, py, pz. (as for vibrations, orbitals that change position = 0,
orbitals that do not change =1; and orbitals that remain in the same position but change
sign = -1)
4. Find the irreducible representations (they correspond to the symmetry of group orbitals, also
called Symmetry Adapted Linear Combinations SALC’s of the orbitals).
5. Find AO’s in central atom with the same symmetry
6. Combine AO’s from central atom with those group orbitals of same symmetry and similar E
F-H-F- D∞h, use D2h
1st consider combinations of
2s and 2p orbitals on F atoms
Obtain the reducible rep
based on equivalent F 2s
orbitals.
G2s
Use Reduction Procedure
to get the irreducible reps.
G2s = Ag + B1u
Use the Projection Operator
to obtain a SALC for each
irreducible rep
Repeat for each group of
equivalent atomic orbitals to obtain
the full set of eight SALC.
2
2
0
0
0
0
2
2
SALC can now be treated similarly to the atomic orbitals
and combined with appropriate AO’s from H
1s(H) is Ag so it matches two SALC.
The interaction can be bonding or antibonding.
Both interactions are symmetry allowed, how about energies?
Orbital potential energies (see also Table 5-1 in p. 134 of textbook)
Average energies for all electrons in the same level, e.g., 3p
(use to estimate which orbitals may interact)
-13.6 eV
Good E match
Strong interaction
-18.65 eV
Poor E match
weak interaction
-40.2 eV
Characterize the electrons: bonding, non-bonding,
antibonding.
Lewis structure
F-H-Fimplies 4 e around H !
MO analysis
defines 3c-2e bond
(2e delocalized over 3 atoms)
Bonding e
Non-bonding e
CO2
D∞h, use D2h
(O O) group orbitals the same as for (F F)!!
But C has more AO’s to
be considered than H !
CO2
D∞h, use D2h
No match
Carbon orbitals
Ag-Ag interactions of C 2s and the SALC of O 2s
-19.43 eV
-32.38 eV
Ag-Ag interactions, now C 2s and the Ag SALC of the C 2pz
-10.66 eV
-19.43 eV
B1u-B1u interactions. Carbon pz with SALC of oxygen 2s
SALC
B1u-B1u interactions. Carbon pz with oxygen pz SALC
Symmetry allows many interactions. Energy
considerations guide as to which is important.
Primary B1u interaction
Primary Ag interaction
SALC of Ag and B1u
SALC of Ag and B1u
Strengths of Interactions
Ag :2s(C); -15.9 --- SALC of 2s(O);– 32.4 : D = 16.5
vs
2s(C) ); -19.4 --- SALC of 2p(O); -15.9: D = 3.5
B1u: 2pz(C); -10.7 --- SALC of 2s(O); -32.4: D = 21.7
vs
2pz(C); -10.7 --- SALC 2p(O); -15.9: D = 5.2
Primary B1u interaction
Primary Ag interaction
Non-bonding p
Bonding p
Bonding s
Non-bonding s
4 bonds
All occupied MO’s are 3c-2e
LUMO
The frontier orbitals of CO2
HOMO
Molecular orbitals for larger molecules: H2O
1. Determine point group of molecule: C2v
2. Assign x, y, z coordinates (z axis is higher rotation axis; if
non-linear y axis in outer atoms point to central atom - not
necessary for H since s orbitals are non-directional)
3. Find the characters of the representation for the combination of 2s orbitals on the outer
atoms, then for px, py, pz. (as for vibrations, orbitals that change position = 0, orbitals
that do not change =1; and orbitals that remain in the same position but change sign = -1)
4. Find the irreducible representations (they correspond to the symmetry of group orbitals,
also called Symmetry Adapted Linear Combinations SALC’s of the orbitals).
5. Find AO’s in central atom with the same symmetry
6. Combine AO’s from central atom with those group orbitals of same symmetry and similar E
G
2
0
2
0
For H H group orbitals
E two orbitals unchanged
C2 two orbitals interchanged
sv two orbitals unchanged
sv’ two orbitals interchanged
G = A1 + B1
No
match
antibonding
a1 sym
antibonding
px
b1 sym
b2 sym
non-bonding
pz
py
slightly
bonding
bonding
bonding
Molecular orbitals for NH3
Find reducible representation for 3H’s
G
3
0
1
Irreducible representations: G = A1 + E
anti-bonding
anti-bonding
LUMO
pz
Slightly
bonding
HOMO
bonding
bonding
Acid-base and donor-acceptor chemistry
Hard and soft acids and bases
Classical concepts
Arrhenius:
• acids form hydrogen ions H+ (hydronium, oxonium H3O+) in aqueous solut
• bases form hydroxide ions OH- in aqueous solution
• acid + base  salt + water
e.g. HNO3 + KOH  KNO3 + H2O
Brønsted-Lowry:
• acids tend to lose H+
• bases tend to gain H+
• acid 1 + base 1  base 1 + acid 2 (conjugate pairs)
H3O+ + NO2-  H2O + HNO2
NH4+ + NH2-  NH3 + NH3
In any solvent, the reaction always favors the formation of the weaker acids or bas
The Lewis concept is more general
and can be interpreted in terms of MO’s
Remember
that frontier orbitals
define the chemistry
of a molecule CO is a s-donor and
a p-acceptor
d+
d-
C
O
M
C
O
C
O
M
Acids and bases (the Lewis concept)
A base is an electron-pair donor
An acid is an electron-pair acceptor
acid
adduct
base
Lewis acid-base adducts involving metal ions
are called coordination compounds (or complexes)
Frontier orbitals and acid-base reactions
Remember the NH3 molecule
Frontier orbitals and acid-base reactions
The protonation of NH3
New LUMO
(nonbonding)
New HOMO
(bonding)
(Td)
(C3v)
In most acid-base reactions HOMO-LUMO combinations
lead to new HOMO-LUMO of the product
But remember that there must be useful overlap (same symmetry)
and similar energies to form new bonding and antibonding orbitals
What reactions take place if energies are very different?
Frontier orbitals and acid-base reactions
Very different energies like A-B or A-E
no adducts form
Similar energies like A-C or A-D
adducts form
A base has an electron-pair
in a HOMO of suitable symmetry
to interact with the LUMO of the acid
The MO basis for hydrogen bonding
F-H-F-
MO diagram derived from atomic orbitals
(using F…….F group orbitals + H orbitals)
Bonding e
Non-bonding e
But it is also possible from HF + F-
First form HF
HOMO-LUMO of HF for s interaction
Non-bonding
(no symmetry match)
Non-bonding
(no E match)
The MO basis for hydrogen bonding
F-H-F-
LUMO
HOMO
Formation of the orbitals
HOMO
HOMO
First take bonding and
antibonding combinations.
Similarly for unsymmetrical B-HA
Total energy of B-H-A
lower than the sum of
the energies of
reactants
Poor energy match,
little or no Hbonding
e.g. CH4 + H2O
Good energy match,
strong H-bonding
e.g. CH3COOH + H2O
Very poor energy match
no adduct formed
H+ transfer reaction
e.g. HCl + H2O
Hard and soft acids and bases
Hard acids or bases are small and non-polarizable
Soft acids and bases are larger and more polarizable
Halide ions increase in softness:
fluoride < chloride<bromide<iodide
Hard-hard or soft-soft interactions are stronger (with less soluble salts)
than hard-soft interactions (which tend to be more soluble).
Most metals are classified as Hard (Class a) acids or acceptors.
Exceptions shown below: acceptors metals in red box are always soft (Class
Other metals are soft in low oxidation states and are indicated by symbol.
Class (b) or soft always Solubilities: AgF > AgCl > AgBr >AgI
But……
LiBr > LiCl > LiI > LiF
Chatt’s explanationClass (b) soft metals have d electrons available for p-bondin
Model: Base donates electron density to metal acceptor. Back donation, from
acid to base, may occur from the d electrons of the acid metal into vacant
orbitals on the base.
Higher oxidation states of elements to the right of transition metals have more class b chara
since there are electrons outside the d shell.
Ex. (Tl(III) > Tl(I), has two 6s electrons outside the 5d making them less available for π-bond
For transition metals:
high oxidation states and position to the left of periodic table are hard
low oxidation states and position to the right of periodic table are soft
Soft donor molecules or ions that are readily polarizable and have vacant d or π* orb
available for π-bonding react best with class (b) soft metals
Tendency to complex with hard metal ions
N >> P > As > Sb
O >> S > Se > Te
F > Cl > Br > I
Tendency to complex with soft metal ions
N << P > As > Sb
O << S > Se ~ Te
F < Cl < Br < I
The hard-soft distinction is linked to polarizability, the degree to which a molecule
or ion may be easily distorted by interaction with other molecules or ions.
Hard acids or bases are small and non-polarizable
Soft acids and bases are larger and more polarizable
Hard acids are cations with high positive charge (3+ or greater),
or cations with d electrons not available for π-bonding
Soft acids are cations with a moderate positive charge (2+ or lower),
Or cations with d electrons readily availbale for π-bonding
The larger and more massive an ion, the softer (large number of internal elec
Shield the outer ones making the atom or ion more polarizable)
For bases, a large number of electrons or a larger size are related to soft cha
Hard acids tend to react better with hard bases and soft acids with
soft bases, in order to produce hard-hard or soft-soft combinations
In general, hard-hard combinations are energetically
more favorable than soft-soft
An acid or a base may be hard or soft
and at the same time it may be strong or weak
Both characteristics must always be taken into account
e.g. If two bases equally soft compete for the same acid,
the one with greater basicity will be preferred
but if they are not equally soft, the preference may be inverted
Fajans’ rules
1. For a given cation, covalent character increases
with increasing anion size. F<Cl<Br<I
2. For a given anion, covalent character increases
with decreasing cation size. K<Na<Li
3. The covalent character increases
with increasing charge on either ion.
4. Covalent character is greater for cations with non-noble gas
electronic configurations.
A greater covalent character resulting from a soft-soft interaction is related
to lower solubility, color and short interionic distances,
whereas hard-hard interactions result in colorless and highly soluble compounds
Quantitative measurements
IA
=
2
Absolute hardness
(Pearson)
s=
I+A
=
2
Mulliken’s absolute electronegativity
(Pearson)
1
EHOMO = -I

ELUMO = -A
Softness
Energy levels
for halogens
and relations between
,  and HOMOLUMO energies